1. Field of the Invention
The present invention relates to robotic manipulators and, more particularly, to a method and means for the reliable and numerically efficient generation of constrained time-optimum trajectories for the simple and compound or blended moves of single-arm, dual-arm, and multi-arm robotic manipulators.
2. Prior Art
Single-arm, dual-arm, and multi-arm, i.e., single end effector, dual end effector, and multi end effector, robotic manipulators are used in various types of transport apparatus in embodiments well known in the prior art. Examples of typical transport apparatus including such embodiments are described in U.S. Pat. Nos. 4,730,976, 5,180,276, 5,404,894, 5,431,529, 5,647,724, 5,655,060, 5,765,983, and in pending U.S. application Ser. No. 09/163,844, the latter having an assignee in common with this application, and the disclosures of all of which are incorporated herein by reference. In an embodiment such as used with a substrate transport apparatus, the transport arms have the end effectors mounted thereon for carrying substrates, such as semiconductor wafers or flat panel displays, through suitable trajectories for processing. The substrate is typically held by means of frictional force between the substrate and the end effector, which force may be supplemented or accompanied by a vacuum or electrostatic holddown in some applications. Therefore, the substrate will slide if the inertial force at the substrate exceeds the holding force securing it to the end effector, so that the transfer time is limited by the magnitude of this holding force. Furthermore, additional constraints, such as limited velocity and jerk, are typically required for safe operation and trajectory tracking reasons. Accordingly, a computationally efficient system that calculates a transfer trajectory without causing the substrate to slide and without violating prescribed constraints is required for maximum substrate throughput levels. In an existing approach, e.g., refer to U.S. Pat. No. 5,655,060, a backward trajectory (backward from the end position of the move) and a forward trajectory (forward from the start position of the move) are calculated iteratively and blended. However, the present state of the available methods, in this exemplary approach and other embodiments, for achieving iterative trajectory generation with the known multi-arm robotic manipulators is fraught with problems. For example, generally among these methods the existence of a reliable solution to the iterative computation is not guaranteed and the calculations are computationally demanding and time consuming, leading to delays, especially in the abort function. Suboptimal acceleration profiles and defective trajectory profiles cause acceleration tracking difficulties and throughput loss. Trajectories change drastically for small variations in departure and destination positions. A large memory is required to store trajectory points, and different settings are required for different arms/speeds.
A number of typical defects that occur with existing trajectory generation in substrate transport apparatus are illustrated in the acceleration vs. time profiles in FIGS. 1-10, with the defects being indicated by circles. Specifically, FIGS. 1-6 variously show radial extension of the arms and FIGS. 7-10 show rotational movement. It will be seen that the smoothness of the acceleration profiles is interrupted at the portions of the curves indicated by the circles.
Another drawback of the existing approach, typified by that in U.S. Pat. No. 5,655,060, is that individual moves must be executed sequentially with no provision for blending simple moves into a single trajectory to create a single smooth transfer path. The sequential execution requires stops between the individual moves and increases the overall travel time.